Numerical Evaluation of Two-Loop Integrals in FDR

Abstract

We present a method to numerically evaluate infrared-finite one- and two-loop integrals within the Four-Dimensional Regularization/Renormalization approach, in which a small mass serves as regulator. Typical integrals exhibit a logarithmic dependence on this mass, which we extract with the aid of suitable subtraction terms that can easily be integrated analytically until the logarithmic structure is revealed. As first physical applications to test the method, we calculate QCD corrections to the decay rates of scalar and pseudoscalar Higgs bosons into two photons in the limit of an infinite top-quark mass as well as to the $\rho$ parameter.